Simplify the following expression and state the condition under which the simplification is valid. $x = \dfrac{n^2 - 64}{n - 8}$
First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = n$ $ b = \sqrt{64} = -8$ So we can rewrite the expression as: $x = \dfrac{({n} {-8})({n} + {8})} {n - 8} $ We can divide the numerator and denominator by $(n - 8)$ on condition that $n \neq 8$ Therefore $x = n + 8; n \neq 8$